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Homomorphic Authenticators

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Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Abstract

Homomorphic authenticators allow to evaluate functions on authenticated data. There exist constructions both in the secret key setting in the form of homomorphic message authentication codes (MACs) and in the public key setting in the form of homomorphic signatures. These solutions can be used to respectively construct privately and publicly verifiable computing schemes. There are homomorphic MAC and signature schemes that are not known to allow verification faster than computing the function, e.g. Gennaro and Wichs (Fully homomorphic message authenticators, in Advances in Cryptology - ASIACRYPT 2013 - 19th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II, Bengaluru, 1–5 December 2013, pp. 301–320) or Freeman (Improved security for linearly homomorphic signatures: a generic framework, in Public Key Cryptography - PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings, Darmstadt, 21–23 May 2012, pp. 697–714), and are therefore not considered in this chapter. In the following, first, we provide the definitions for schemes using homomorphic authenticators and their correctness and security. Then we present privately verifiable computing schemes using MACs, i.e. “Verifiable Delegation of Computation on Outsourced Data” by Backes et al., “Generalized Homomorphic MACs with Efficient Verification” by Zhang and Safavi-Naini, and “Efficiently Verifiable Computation on Encrypted Data” by Fiore et al. Afterwards, we present the publicly verifiable computing schemes using homomorphic signatures, i.e. “Programmable Hash Functions Go Private” by Catalano et al., “Homomorphic Signatures with Efficient Verification for Polynomial Functions” by Catalano et al., and “Algebraic (Trapdoor) One-Way Functions and their Applications” by Catalano et al. Finally, we present an approach by Lai et al., “Verifiable Computation on Outsourced Encrypted Data”, showing how to combine signature based verifiable computing with homomorphic encryption assuring privacy of the data processed.

Keywords

Signature Scheme Homomorphic Encryption Semantic Security Homomorphic Encryption Scheme Verifiable Computation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    M. Backes, D. Fiore, R.M. Reischuk, Verifiable delegation of computation on outsourced data, in 2013 ACM SIGSAC Conference on Computer and Communications Security, CCS’13, Berlin, 4–8 November 2013, pp. 863–874Google Scholar
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    D. Boneh, D.M. Freeman, J. Katz, B. Waters, Signing a linear subspace: signature schemes for network coding, in Public Key Cryptography - PKC 2009, 12th International Conference on Practice and Theory in Public Key Cryptography, Proceedings, Irvine, CA, 18–20 March 2009, pp. 68–87Google Scholar
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    D. Catalano, D. Fiore, R. Gennaro, K. Vamvourellis, Algebraic (trapdoor) one-way functions and their applications, in TCC (2013), pp. 680–699Google Scholar
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    D. Catalano, D. Fiore, B. Warinschi, Homomorphic signatures with efficient verification for polynomial functions, in Advances in Cryptology - CRYPTO 2014 - 34th Annual Cryptology Conference, Proceedings, Part I, Santa Barbara, CA, 17–21 August 2014, pp. 371–389Google Scholar
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    D. Catalano, D. Fiore, L. Nizzardo, Programmable hash functions go private: constructions and applications to (homomorphic) signatures with shorter public keys, in Advances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Proceedings, Part II, Santa Barbara, CA, 16–20 August 2015, pp. 254–274Google Scholar
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    D. Fiore, R. Gennaro, V. Pastro, Efficiently verifiable computation on encrypted data, in Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, Scottsdale, AZ, 3–7 November 2014, pp. 844–855Google Scholar
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    D.M. Freeman, Improved security for linearly homomorphic signatures: a generic framework, in Public Key Cryptography - PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings, Darmstadt, 21–23 May 2012, pp. 697–714Google Scholar
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    R. Gennaro, D. Wichs, Fully homomorphic message authenticators, in Advances in Cryptology - ASIACRYPT 2013 - 19th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II, Bengaluru, 1–5 December 2013, pp. 301–320Google Scholar
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    J. Lai, R.H. Deng, H. Pang, J. Weng, Verifiable computation on outsourced encrypted data, in Computer Security - ESORICS 2014 - 19th European Symposium on Research in Computer Security, Proceedings, Part I, Wroclaw, 7–11 September 2014, pp. 273–291Google Scholar
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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Theoretische InformatikTechnische Universität DarmstadtDarmstadtGermany

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